 Lesson

## Ideas

We have looked at a number of ways to solve  quadratic equations  . These include:

•  Factorising  the quadratic expression and then using the null factor law. In particular, when the quadratic expression is non-monic, we can use techniques for non-monic quadratic trinomials.

• Completing the square and then taking the square root of both sides of the equation.

• Using the  quadratic formula  .

### Examples

#### Example 1

Solve 5x^{2}+22x+8=0 for x by factorising or otherwise.

Worked Solution
Create a strategy

Factorise the equation and then solve for x.

Apply the idea

So the solutions are x=-\dfrac{2}{5},\,x=-4.

#### Example 2

Solve 4x^{2}+11x+7=0 for x by completing the square or otherwise.

Worked Solution
Create a strategy

Use completing the square.

Apply the idea

So the solutions are x=-1,\,x=-\dfrac{7}{4}.

#### Example 3

Solve 4x^{2}+7x+3=0 for x by using the quadratic formula or otherwise.

Worked Solution
Create a strategy

We can use the quadratic formula: x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}.

Apply the idea

So the solutions are x=-\dfrac{3}{4},\,x=-1.

Idea summary

• Factorising the quadratic expression and then using the null factor law.

• Completing the square.